urextremeI {Runuran} | R Documentation |
UNU.RAN Extreme value type I (Gumbel-type) random variate generator
Description
UNU.RAN random variate generator for the Extreme value type I
(Gumbel-type) distribution with
location parameter location
and scale parameter scale
.
It also allows sampling from the truncated distribution.
[Special Generator] – Sampling Function: Gumbel (extreme value type I).
Usage
urextremeI(n, location=0, scale=1, lb=-Inf, ub=Inf)
Arguments
n |
size of required sample. |
location |
location parameter. |
scale |
(strictly positive) scale parameter. |
lb |
lower bound of (truncated) distribution. |
ub |
upper bound of (truncated) distribution. |
Details
If location
or scale
are not specified, they assume
the default values of 0
and 1
respectively.
The Gumbel distribution with location l
and scale s
has
distribution function
F(x) = \exp(-\exp(-\frac{x-l}{s}))
for all x
.
The generation algorithm uses fast numerical inversion. The parameters
lb
and ub
can be used to generate variates from
the Gumbel distribution truncated to the interval (lb
,ub
).
Note
This function is wrapper for the UNU.RAN class in R.
Author(s)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
References
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg.
N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap.22, p.2.
See Also
runif
and .Random.seed
about random number
generation and unuran
for the UNU.RAN class.
Examples
## Create a sample of size 1000
x <- urextremeI(n=1000)